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    <title>OREKIT</title>
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    <h1>1. Purpose</h1>

    <p>OREKIT library is a low-level library for space mechanics projects. It is
      implemented in the JAVA language.</p>

    <p>OREKIT project was initiated by CS with the following goals in mind:</p>

    <ul>
      <li>provide a common base layer for space projects</li>
      <li>support both quick developments with loose requirements and complex projects with rich
        physical modeling, fine customization, and high accuracy</li>
      <li>be user-extensible through clear and as simple as possible architecture</li>
      <li>use unified interfaces to allow models and algorithms switching with almost no effort</li>
      <li>provide both basic and rich models that can be plugged interchangeably to ease
        applications validation</li>
      <li>separate models configuration from models usage to hide away complexity and keep caller
        code simple</li>
      <li>support both development of standalone and embedded applications (web services, plugins,
        scripting frameworks...)</li>
      <li>use up-to-date techniques for low cost development and maintenance</li>
      <li>remove platforms and system dependencies and leverage environment-hell (environment
        variables, dynamic libraries versions, operating system, filesystem layout...)</li>
    </ul>

    <h1>2. Features</h1>

    <p>Orekit can be used for many purposes, from simple geometrical or orbital tools up to complex
      orbits propagators with several perturbing forces, maneuvers and discrete events. Here is
      a short list of the features offered by the library:</p>

    <ul>
      <li>Time
        <ul>
          <li>high accuracy absolute dates</li>
          <li>time scales (TAI, UTC, UT1, GPS, TT, TCG, TDB, TCB, GMST, GST, GLONASS, QZSS, BDT,
            IRNSS...)</li>
          <li>transparent handling of leap seconds</li>
          <li>support for CCSDS time code standards</li>
        </ul>
      </li>
      <li>Geometry
        <ul>
          <li>frames hierarchy supporting fixed and time-dependent (or telemetry-dependent) frames</li>
          <li>predefined frames (EME2000/J2000, ICRF, GCRF, all ITRF from 1988 to 2020 and
            intermediate frames, TOD, MOD, GTOD and TEME frames, Veis, topocentric, tnw and qsw
            local orbital frames, relative encounter frames, Moon, Sun, planets, solar system
            barycenter, Earth-Moon barycenter, ecliptic)</li>
          <li>user extensible (used operationally in real time with a set of about 60 frames on
            several spacecraft)</li>
          <li>transparent handling of IERS Earth Orientation Parameters (for both new CIO-based
            frames following IERS 2010 conventions and old equinox-based frames)</li>
          <li>transparent handling of JPL DE 4xx (405, 406 and more recent) and INPOP ephemerides</li>
          <li>transforms including kinematic combination effects</li>
          <li>composite transforms reduction and caching for efficiency</li>
          <li>extensible central body shapes models (with predefined spherical and ellipsoidic
            shapes)</li>
          <li>cartesian and geodesic coordinates, kinematics</li>
          <li>computation of Dilution Of Precision (DOP) with respect to GNSS constellations</li>
          <li>projection of sensor Field Of View footprint on ground for any FoV shape</li>
        </ul>
      </li>
      <li>Spacecraft state
        <ul>
          <li>cartesian, elliptical Keplerian, circular and equinoctial parameters, with
            non-Keplerian derivatives if available</li>
          <li>Walker constellations (including in-orbit spares with shifted position)</li>
          <li>Two-Line Elements (TLE)</li>
          <li>Two-Line Elements generation using Fixed-Point algorithm or Least Squares Fitting</li>
          <li>transparent conversion between all parameters</li>
          <li>automatic binding with frames</li>
          <li>attitude state and derivative</li>
          <li>jacobians</li>
          <li>mass management</li>
          <li>user-defined associated state (for example battery status, or higher order
            derivatives, or anything else)</li>
        </ul>
      </li>
      <li>Covariance
        <ul>
          <li>covariance propagation</li>
          <li>covariance extrapolation using a Keplerian model</li>
          <li>covariance frame transformation (inertial, Earth fixed, and local orbital frames)</li>
          <li>covariance type transformation (cartesian, keplerian, circular, and equinoctial)</li>
          <li>covariance interpolation based on the blending model</li>
        </ul>
      </li>
      <li>Maneuvers
        <ul>
          <li>analytical models for small maneuvers without propagation</li>
          <li>impulse maneuvers for any propagator type</li>
          <li>continuous maneuvers for numerical propagator type</li>
          <li>configurable low thrust maneuver model based on event detectors</li>
          <li>used-defined propulsion models intended to be used with maneuver class (constant and
            piecewise polynomials already provided by the library)</li>
          <li>user-friendly interface for maneuver triggers</li>
        </ul>
      </li>
      <li>Propagation
        <ul>
          <li>analytical propagation models
            <ul>
              <li>Kepler</li>
              <li>Eckstein-Heschler</li>
              <li>Brouwer-Lyddane with Warren Phipps' correction for the critical inclination of
                63.4° and the perturbative acceleration due to atmospheric drag</li>
              <li>SDP4/SGP4 with 2006 corrections</li>
              <li>GNSS: GPS, QZSS, Galileo, GLONASS, Beidou, IRNSS and SBAS</li>
              <li>Intelsat's 11 elements</li>
            </ul>
          </li>
          <li>numerical propagators
            <ul>
              <li>central attraction</li>
              <li>gravity models including time-dependent like trends and pulsations (automatic
                reading of ICGEM (new Eigen models), SHM (old Eigen models), EGM,
                SHA (GRGM1200B and GRGM1200L) and GRGS gravity field files formats, even compressed)</li>
              <li>atmospheric drag</li>
              <li>third body attraction (with data for Sun, Moon and all solar systems planets)</li>
              <li>radiation pressure with eclipses (multiple oblate spheroids occulting bodies,
                multiple coefficients for bow and wing models)</li>
              <li>solid tides, with or without solid pole tide</li>
              <li>ocean tides, with or without ocean pole tide</li>
              <li>general relativity (including Lense-Thirring and De Sitter corrections)</li>
              <li>Earth's albedo and infrared</li>
              <li>multiple maneuvers</li>
              <li>empirical accelerations to account for the unmodeled forces</li>
              <li>state of the art ODE integrators (adaptive stepsize with error control, continuous
                output, switching functions, G-stop, step normalization...)</li>
              <li>serialization mechanism to store complete results on persistent storage for later
                use</li>
              <li>propagation in non-inertial frames (e.g. for Lagrange point halo orbits)</li>
            </ul>
          </li>
          <li>semi-analytical propagation model (DSST) with customizable force models
            <ul>
              <li>central attraction</li>
              <li>gravity models</li>
              <li>J2-squared effect (Zeis model)</li>
              <li>atmospheric drag</li>
              <li>third body attraction</li>
              <li>radiation pressure with eclipse</li>
            </ul>
          </li>
          <li>computation of Jacobians with respect to orbital parameters and selected force models
            parameters</li>
          <li>trajectories around Lagragian points using CR3BP model</li>
          <li>tabulated ephemerides
            <ul>
              <li>file based</li>
              <li>memory based</li>
              <li>integration based</li>
            </ul>
          </li>
          <li>Taylor-algebra (or any other real field) version of most of the above propagators,
            with all force models, events detection, orbits types, coordinates types and frames
            allowing high order uncertainties and derivatives computation or very fast Monte-Carlo
            analyzes</li>
          <li>unified interface above analytical/numerical/tabulated propagators for easy switch
            from coarse analysis to fine simulation with one line change</li>
          <li>all propagators can manage the time loop by themselves and handle callback functions
            (called step handlers) from the calling application at each time step
            <ul>
              <li>step handlers can be called at discrete time at regular time steps, which are
                independent of propagator time steps</li>
              <li>step handlers can be called with interpolators valid throughout one propagator
                time step, which can have varying sizes </li>
              <li>step handlers can be switched off completely, when only final state is desired</li>
              <li>special step handlers are provided for a posteriori ephemeris generation: all
                intermediate results are stored during propagation and provided back to the application
                which can navigate at will through them, effectively using the propagated orbit as if
                it was analytical model, even if it really is a numerically propagated one, which
                is ideal for search and iterative algorithms</li>
              <li>several step handlers can be used simultaneously, so it is possible to have a fine
                grained fixed time step to log state in a huge file, and have at the same time
                a coarse grained time step to display progress for user at a more human-friendly
                rate, this feature can also be used for debugging purpose, by setting up a temporary
                step handler alongside the operational ones</li>
            </ul>
          </li>
          <li>handling of discrete events during integration (models changes, G-stop, simple
            notifications...)</li>
          <li>adaptable max checking interval for discrete events detection</li>
          <li>predefined discrete events
            <ul>
              <li>eclipse (both umbra and penumbra)</li>
              <li>ascending and descending node crossing</li>
              <li>anomaly, latitude argument or longitude argument crossings, with either true,
                eccentric or mean angles</li>
              <li>apogee and perigee crossing</li>
              <li>alignment with some body in the orbital plane (with customizable threshold angle)</li>
              <li>angular separation thresholds crossing between spacecraft and a beacon (typically
                the Sun) as seen from an observer (typically a ground station)</li>
              <li>raising/setting with respect to a ground location (with customizable triggering
                elevation and ground mask, optionally considering refraction)</li>
              <li>date and on-the-fly resetting countdown</li>
              <li>date interval with parameter-driven boundaries</li>
              <li>latitude, longitude, altitude crossing</li>
              <li>latitude, longitude extremum</li>
              <li>elevation extremum</li>
              <li>moving target detection (with optional radius) in spacecraft sensor Field Of View
                (any shape, with special case for circular)</li>
              <li>spacecraft detection in ground based Field Of View (any shape)</li>
              <li>sensor Field Of View (any shape) overlapping complex geographic zone</li>
              <li>complex geographic zones traversal</li>
              <li>inter-satellites direct view (with customizable skimming altitude)</li>
              <li>ground at night</li>
              <li>impulse maneuvers occurrence</li>
              <li>geomagnetic intensity</li>
  	          <li>extremum approach for TCA (Time of Closest Approach) computing</li>
              <li>beta angle</li>
              <li>relative distance with another object</li>
            </ul>
          </li>
          <li>possibility of slightly shifting events in time (for example to switch from solar
            pointing mode to something else a few minutes before eclipse entry and reverting to
            solar pointing mode a few minutes after eclipse exit)</li>
          <li>events filtering based on their direction (for example to detect only eclipse entries
            and not eclipse exits)</li>
          <li>events filtering based on an external enabling function (for example to detect events
            only during selected orbits and not others)</li>
          <li>events combination with boolean operators</li>
          <li>ability to run several propagators in parallel and manage their states simultaneously
            throughout propagation</li>
        </ul>
      </li>
      <li>Attitude
        <ul>
          <li>extensible attitude evolution models</li>
          <li>predefined laws
            <ul>
              <li>central body related attitude (nadir pointing, center pointing, target pointing,
                yaw compensation, yaw-steering)</li>
              <li>orbit referenced attitudes (LOF aligned, offset on all axes)</li>
              <li>space referenced attitudes (inertial, celestial body-pointed, spin-stabilized)</li>
              <li>attitude aligned with one target and constrained by another target</li>
              <li>tabulated attitudes, either respective to inertial frame or respective to Local
                Orbital Frames</li>
              <li>specific law for GNSS satellites: GPS (block IIA, block IIF, block IIF),
                GLONASS, GALILEO, BEIDOU (GEO, IGSO, MEO)</li>
              <li>torque-free for general (non-symmetrical) body</li>
            </ul>
          </li>
          <li>loading and writing of CCSDS Attitude Data Messages (both AEM, APM and ACM types are
            supported, in both KVN and XML formats, standalone or in combined NDM)</li>
          <li>exporting of attitude ephemeris in CCSDS AEM and ACM file format</li>
        </ul>
      </li>
      <li>Orbit determination
        <ul>
          <li>batch least squares fitting
            <ul>
              <li>optimizers choice (Levenberg-Marquardt or Gauss-Newton)</li>
              <li>decomposition algorithms choice (QR, LU, SVD, Cholesky)</li>
              <li>choice between forming normal equations or not</li>
            </ul>
          </li>
          <li>sequential batch least squares
            <ul>
              <li>sequential Gauss-Newton optimizer</li>
              <li>decomposition algorithms choice (QR, LU, SVD, Cholesky)</li>
              <li>possibility to use an initial covariance matrix</li>
            </ul>
          </li>
          <li>Kalman filtering
            <ul>
              <li>customizable process noise matrices providers</li>
              <li>time dependent process noise provider</li>
              <li>implementation of the Extended Kalman Filter</li>
              <li>implementation of the Extended Semi-analytical Kalman Filter (ESKF)</li>
  	          <li>implementation of the Unscented Kalman Filter</li>
  	          <li>implementation of the Unscented Semi-analytical Kalman Filter</li>
            </ul>
          </li>
          <li>parameters estimation
            <ul>
              <li>orbital parameters estimation (or only a subset if desired)</li>
              <li>force model parameters estimation (drag coefficients, radiation pressure
                coefficients, central attraction, maneuver thrust, flow rate or start/stop epoch)</li>
              <li>measurements parameters estimation (biases, satellite clock offset, station clock
                offset, station position, pole motion and rate, prime meridian correction and rate,
                total zenith delay in tropospheric correction)</li>
            </ul>
          </li>
          <li>orbit determination can be performed with numerical, DSST, SDP4/SGP4,
            Eckstein-Hechler, Brouwer-Lyddane, or Keplerian propagators</li>
          <li>ephemeris-based orbit determination to estimate measurement parameters like station
            biases or clock offsets</li>
          <li>multi-satellites orbit determination</li>
          <li>initial orbit determination methods (Gibbs, Gooding, Lambert, Gauss, and Laplace)</li>
          <li>ground stations displacements due to solid tides</li>
          <li>ground stations displacements due to ocean loading (based on Onsala Space Observatory
            files in BLQ format)</li>
          <li>ground stations displacements due to plate tectonics</li>
          <li>several predefined measurements
            <ul>
              <li>range</li>
              <li>range rate (one way and two way)</li>
              <li>turn-around range</li>
              <li>azimuth/elevation</li>
              <li>right ascension/declination</li>
              <li>position-velocity</li>
              <li>position</li>
              <li>inter-satellites range (one way and two way)</li>
              <li>inter-satellites GNSS one way range rate</li>
              <li>inter-satellites GNSS phase</li>
              <li>GNSS code</li>
              <li>GNSS phase with integer ambiguity resolution and wind-up effect</li>
              <li>Time Difference of Arrival (TDOA)</li>
              <li>Frequency Difference of Arrival (FDOA)</li>
              <li>Bi-static range and range rate</li>
              <li>multiplexed</li>
            </ul>
          </li>
          <li>possibility to add custom measurements</li>
          <li>loading of ILRS CRD laser ranging measurements file</li>
          <li>loading and writing of CCSDS Tracking Data Messages (in both KVN and XML formats,
            standalone or in combined NDM)</li>
          <li>several predefined modifiers
            <ul>
              <li>tropospheric effects</li>
              <li>ionospheric effects</li>
              <li>clock relativistic effects (including J2 correction)</li>
              <li>station offsets</li>
              <li>biases</li>
              <li>delays</li>
              <li>Antenna Phase Center</li>
              <li>Phase ambiguity</li>
              <li>Shapiro relativistic effect</li>
              <li>aberration of light in telescope measurements</li>
            </ul>
          </li>
          <li>possibility to add custom measurement modifiers (even for predefined events)</li>
          <li>combination of GNSS measurements
            <ul>
              <li>dual frequency combination of measurements (Geometry-free, Ionosphere-free,
                Narrow-lane, Wide-lane and Melbourne-Wübbena)</li>
              <li>single frequency combination of measurements (Phase minus code and GRAPHIC)</li>
            </ul>
          </li>
          <li>measurements generation
            <ul>
              <li>with measurements feasibility triggered by regular event detectors (ground
                visibility, ground at night, sunlit satellite, inter satellites direct view, boolean
                combination...)</li>
              <li>with measurement scheduling as fixed step streams (optionally aligned with round
                UTC time)</li>
              <li>with measurement scheduling as high rate bursts rest periods (optionally aligned
                with round UTC time)</li>
              <li>possibility to customize measurement scheduling</li>
            </ul>
          </li>
        </ul>
      </li>
      <li>GNSS
        <ul>
          <li>computation of Dilution Of Precision</li>
          <li>loading of ANTEX antenna models file</li>
          <li>loading and writing of RINEX observation files (version 2, 3, and 4)</li>
          <li>loading of RINEX navigation files (version 2, 3, and 4)</li>
          <li>support for Hatanaka compact RINEX format</li>
          <li>loading of SINEX file (can load station positions, velocities, eccentricities,
            Post-Seismic Deformation models, EOPs, and Differential Code Biases)</li>
          <li>loading of RINEX clock files (version 2 and version 3)</li>
          <li>parsing of IGS SSR messages for all constellations (version 1)</li>
          <li>parsing of RTCM messages (both ephemeris and correction messages)</li>
          <li>parsing of GPS RF link binary message</li>
          <li>Hatch filters for GNSS measurements smoothing</li>
          <li>implementation of Ntrip protocol</li>
          <li>decoding of GPS navigation messages</li>
        </ul>
      </li>
      <li>Orbit file handling
        <ul>
          <li>loading and writing of SP3 orbit files (from versions a to d, including extension to a few inertial frames)</li>
          <li>splicing and interpolation of SP3 files</li>
          <li>loading and writing of CCSDS Orbit Data Messages (both OPM, OEM, OMM, OCM types are
            supported, in both KVN and XML formats, standalone or in combined NDM)</li>
          <li>loading of SEM and YUMA files for GPS constellation</li>
          <li>exporting of ephemeris in CCSDS OEM and OCM file formats</li>
          <li>loading of ILRS CPF orbit files</li>
          <li>exporting of ephemeris in STK format</li>
        </ul>
      </li>
      <li>Earth models
        <ul>
          <li>atmospheric models (DTM2000, Jacchia-Bowman 2008, NRL MSISE 2000, Harris-Priester and
            simple exponential models), and Marshall solar Activity Future Estimation, optionally
            with lift component</li>
          <li>support for CSSI space weather data</li>
          <li>support for SOLFSMY and DTC data for JB2008 atmospheric model</li>
          <li>tropospheric delay (modified Saastamoinen, estimated, fixed)</li>
          <li>tropospheric mapping functions (Vienna 1, Vienna 3, Global, Niell)</li>
          <li>tropospheric refraction correction angle (Recommendation ITU-R P.834-7 and
            Saemundssen's formula quoted by Meeus)</li>
          <li>tropospheric model for laser ranging (Marini-Murray, Mendes-Pavlis)</li>
          <li>Klobuchar ionospheric model (including parsing α and β coefficients from University of
            Bern Astronomical Institute files)</li>
          <li>Global Ionospheric Map (GIM) model</li>
          <li>NeQuick ionospheric model</li>
          <li>VTEC estimated ionospheric model with Single Layer Model (SLM) ionospheric mapping
            function</li>
          <li>Global Pressure and Temperature models (GPT, GPT2, GPT2w, GPT3)</li>
          <li>geomagnetic field (WMM, IGRF)</li>
          <li>geoid model from any gravity field</li>
          <li>displacement of ground points due to tides</li>
          <li>tessellation of zones of interest as tiles</li>
          <li>sampling of zones of interest as grids of points</li>
          <li>construction of trajectories using loxodromes (commonly, a rhumb line)</li>
        </ul>
      </li>
      <li>Indirect optimal control
        <ul>
          <li>adjoint equations as defined by Pontryagin's Maximum Principle with Cartesian coordinates for a range of forces: (gravitational, inertial) including J2</li>
          <li>so-called energy cost functions (proportional to the integral of the control vector's squared norm), with Hamitonian evaluation</li>
          <li>single shooting based on Newton algorithm for the case of fixed time, fixed Cartesian bounds</li>
        </ul>
      </li>
      <li>Collisions
        <ul>
          <li>loading and writing of CCSDS Conjunction Data Messages (CDM in both KVN and XML
            formats)</li>
          <li>2D probability of collision computing methods assuming short term encounter and
            spherical bodies:
            <ul>
              <li>Chan 1997</li>
              <li>Alfriend 1999</li>
              <li>Alfriend 1999 (maximum version)</li>
              <li>Alfano 2005</li>
              <li>Patera 2005 (custom Orekit implementation) (recommended)</li>
              <li>Laas 2015 (recommended)</li>
            </ul></li>
        </ul>
      </li>
      <li>Customizable data loading
        <ul>
          <li>loading by exploring folders hierarchy on local disk</li>
          <li>loading from explicit lists of files on local disk</li>
          <li>loading from classpath</li>
          <li>loading from network (even through internet proxies)</li>
          <li>support for zip archives</li>
          <li>automatic decompression of gzip compressed (.gz) files upon loading</li>
          <li>automatic decompression of Unix compressed (.Z) files upon loading</li>
          <li>automatic decompression of Hatanaka compressed files upon loading</li>
          <li>plugin mechanism to add filtering like custom decompression algorithms, deciphering or
            monitoring</li>
          <li>plugin mechanism to delegate loading to user defined database or data access library</li>
        </ul>
      </li>
    </ul>

    <h1>3. Dependency</h1>

    <p>OREKIT has only one dependency: the <a href="https://hipparchus.org/">Hipparchus</a>
      open-source library. This library provides mathematical tools for many purposes: geometry,
      polynomial equations, differential equations, and more... It is distributed under the
      business-friendly Apache Software License version 2.0.</p>

    <p>OREKIT is based on several Hipparchus packages:</p>

    <ul>
      <li>geometry, which provides very useful objects as vectors and rotations (internally
        represented by quaternions)</li>
      <li>ode, which provides numerical solutions to solve Ordinary Differential Equations (ODE)</li>
      <li>optim, which provides multi-dimensional optimization</li>
      <li>solvers, which provides root-finding algorithms</li>
      <li>differentiation, which provides analytical computation of partial derivatives to arbitrary
        order and arbitrary number of free parameters</li>
    </ul>

    <p>The use of Hipparchus is hidden in OREKIT as much as possible so users don't need to fully
      master this library. If they wish, they can limit themselves to understanding the simple
      classes Vector3D and Rotation from the geometry package, and the interface
      FirstOrderIntegrator from the ode package.</p>

    @author Luc Maisonobe
    @author Thierry Ceolin
    @author Fabien Maussion
    @author Pascal Parraud
    @author Véronique Pommier-Maurussane
    @author Guylaine Prat

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